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  1. solariiknight(ஆனந்த்) (solariiknight@social.systemreboot.net)'s status on Sunday, 10-Dec-2017 12:18:12 EST solariiknight(ஆனந்த்) solariiknight(ஆனந்த்)
    The Gambler's fallacy:
    I fall for this fallacy when playing battle for Wesnoth - if my unit misses several times, I assume that it will hit more frequently the next few times. https://social.systemreboot.net/attachment/70815
    In conversation Sunday, 10-Dec-2017 12:18:12 EST from social.systemreboot.net permalink
    1. Bob Jonkman (bobjonkman@gs.jonkman.ca)'s status on Monday, 11-Dec-2017 02:42:09 EST Bob Jonkman Bob Jonkman
      in reply to
      That's not incorrect. If your unit misses several times, then you should expect to hit more frequently after a run of misses, assuming your normal average of hits is greater than zero.
      In conversation Monday, 11-Dec-2017 02:42:09 EST from web permalink
      1. solariiknight(ஆனந்த்) (solariiknight@social.systemreboot.net)'s status on Monday, 11-Dec-2017 07:35:40 EST solariiknight(ஆனந்த்) solariiknight(ஆனந்த்)
        in reply to
        Lets take an example. Suppose if my spearman has a 60% chance to hit an horseman. There's a 6.4% probability to miss in all three turns and 21.6% to hit in all three turns. Suppose my spearman misses all three turns, then how does the probability to hit in all three turns increase?
        In conversation Monday, 11-Dec-2017 07:35:40 EST from social.systemreboot.net permalink
        1. solariiknight(ஆனந்த்) (solariiknight@social.systemreboot.net)'s status on Monday, 11-Dec-2017 07:36:27 EST solariiknight(ஆனந்த்) solariiknight(ஆனந்த்)
          in reply to
          * replace turn by attempt. There's 3 attempts per turn.
          In conversation Monday, 11-Dec-2017 07:36:27 EST from social.systemreboot.net permalink
        2. Bob Jonkman (bobjonkman@gs.jonkman.ca)'s status on Monday, 11-Dec-2017 15:57:56 EST Bob Jonkman Bob Jonkman
          in reply to
          If you've got a 6.4% probability to miss in all three turns, then for the next three turns I would expect a 93% probability of getting at least one hit -- much higher than the probability of missing three turns in a row again!
          In conversation Monday, 11-Dec-2017 15:57:56 EST from web permalink
          1. Bob Jonkman (bobjonkman@gs.jonkman.ca)'s status on Monday, 11-Dec-2017 15:59:00 EST Bob Jonkman Bob Jonkman
            in reply to
            93.6% in fact. I'm having a 50% probability of errors while mathing today.
            In conversation Monday, 11-Dec-2017 15:59:00 EST from web permalink
          2. arunisaac (arunisaac@social.systemreboot.net)'s status on Tuesday, 12-Dec-2017 08:05:19 EST arunisaac arunisaac
            in reply to
            @solariiknight said "hit more frequently the next few times". We are interpreting this phrase differently. Hence, the apparent confusion.

            You are comparing the probability of hitting AT LEAST ONCE to the probability of missing THREE times in a row.

            @solariiknight and I are stating that the probability to hit in the next attempt is still 60%, and has not been affected by the result of the previous attempts.
            In conversation Tuesday, 12-Dec-2017 08:05:19 EST from social.systemreboot.net permalink
            1. arunisaac (arunisaac@social.systemreboot.net)'s status on Tuesday, 12-Dec-2017 08:09:03 EST arunisaac arunisaac
              in reply to
              > FOR THE NEXT THREE TURNS I would expect a 93.6% probability of getting at least one hit

              The probability of getting at least one hit is 93.6% for ANY three attempts, regardless of whether those attempts are consecutive, come before/after some other event, etc. Each attack attempt is completely independent and uncorrelated with the result of any other attack attempt.
              In conversation Tuesday, 12-Dec-2017 08:09:03 EST from social.systemreboot.net permalink
      2. arunisaac (arunisaac@social.systemreboot.net)'s status on Monday, 11-Dec-2017 07:57:25 EST arunisaac arunisaac
        in reply to
        Say, you have a coin (assume unbiased) in your pocket, and you toss it. The probability of getting a heads is 50% regardless of that coin's tossing history with a previous owner. Your current toss is independent of all previous tosses.
        In conversation Monday, 11-Dec-2017 07:57:25 EST from social.systemreboot.net permalink
        1. Bob Jonkman (bobjonkman@gs.jonkman.ca)'s status on Monday, 11-Dec-2017 15:55:34 EST Bob Jonkman Bob Jonkman
          in reply to
          Exactly! So if your typical hit rate is 50%, but you have a run of misses, then for the next run I would expect a hit rate of 50% -- much higher than your previous run of misses! :-)
          In conversation Monday, 11-Dec-2017 15:55:34 EST from web permalink
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